Preheat your grill or grill pan over medium heat. Brush the chicken breasts with olive oil and season with salt and pepper. Grill the chicken for about 6-7 minutes on each side, or until fully cooked and no longer pink in the center. Remove from heat and let rest for a few minutes before slicing.
In a small bowl, combine the mashed avocado and lime juice. Mix until smooth and set aside.
Heat a skillet over medium heat. Butter one side of each slice of bread. Place two slices, butter-side down, in the skillet.
Spread half of the avocado mixture on each slice of bread in the skillet. Layer with sliced grilled chicken, spinach leaves, tomato slices, and top with a slice of cheddar cheese.
Place the remaining slices of bread on top, butter-side up. Cook for about 3-4 minutes, or until the bottom is golden brown. Carefully flip the sandwiches and cook for another 3-4 minutes until the other side is golden and the cheese is melted.
Remove from the skillet, slice in half, and serve warm.